2,919 research outputs found
Aerodynamic Stability of Satellites in Elliptic Low Earth Orbits
Topical observations of the thermosphere at altitudes below are
of great benefit in advancing the understanding of the global distribution of
mass, composition, and dynamical responses to geomagnetic forcing, and momentum
transfer via waves. The perceived risks associated with such low altitude and
short duration orbits has prohibited the launch of Discovery-class missions.
Miniaturization of instruments such as mass spectrometers and advances in the
nano-satellite technology, associated with relatively low cost of
nano-satellite manufacturing and operation, open an avenue for performing low
altitude missions. The time dependent coefficients of a second order
non-homogeneous ODE which describes the motion have a double periodic shape.
Hence, they will be approximated using Jacobi elliptic functions. Through a
change of variables the original ODE will be converted into Hill's ODE for
stability analysis using Floquet theory. We are interested in how changes in
the coefficients of the ODE affect the stability of the solution. The expected
result will be an allowable range of parameters for which the motion is
dynamically stable. A possible extension of the application is a computational
tool for the rapid evaluation of the stability of entry or re-entry vehicles in
rarefied flow regimes and of satellites flying in relatively low orbits.Comment: 18 pages, 16 figure
Numerical product design: Springback prediction, compensation and optimization
Numerical simulations are being deployed widely for product design. However, the accuracy of the numerical tools is not yet always sufficiently accurate and reliable. This article focuses on the current state and recent developments in different stages of product design: springback prediction, springback compensation and optimization by finite element (FE) analysis. To improve the springback prediction by FE analysis, guidelines regarding the mesh discretization are provided and a new through-thickness integration scheme for shell elements is launched. In the next stage of virtual product design the product is compensated for springback. Currently, deformations due to springback are manually compensated in the industry. Here, a procedure to automatically compensate the tool geometry, including the CAD description, is presented and it is successfully applied to an industrial automotive part. The last stage in virtual product design comprises optimization. This article presents an optimization scheme which is capable of designing optimal and robust metal forming processes efficiently
Fast Ewald summation for electrostatic potentials with arbitrary periodicity
A unified treatment for fast and spectrally accurate evaluation of
electrostatic potentials subject to periodic boundary conditions in any or none
of the three space dimensions is presented. Ewald decomposition is used to
split the problem into a real space and a Fourier space part, and the FFT based
Spectral Ewald (SE) method is used to accelerate the computation of the latter.
A key component in the unified treatment is an FFT based solution technique for
the free-space Poisson problem in three, two or one dimensions, depending on
the number of non-periodic directions. The cost of calculations is furthermore
reduced by employing an adaptive FFT for the doubly and singly periodic cases,
allowing for different local upsampling rates. The SE method will always be
most efficient for the triply periodic case as the cost for computing FFTs will
be the smallest, whereas the computational cost for the rest of the algorithm
is essentially independent of the periodicity. We show that the cost of
removing periodic boundary conditions from one or two directions out of three
will only marginally increase the total run time. Our comparisons also show
that the computational cost of the SE method for the free-space case is
typically about four times more expensive as compared to the triply periodic
case. The Gaussian window function previously used in the SE method, is here
compared to an approximation of the Kaiser-Bessel window function, recently
introduced. With a carefully tuned shape parameter that is selected based on an
error estimate for this new window function, runtimes for the SE method can be
further reduced. Keywords: Fast Ewald summation, Fast Fourier transform,
Arbitrary periodicity, Coulomb potentials, Adaptive FFT, Fourier integral,
Spectral accuracy.Comment: 21 pages, 11 figure
Fixed Scale Approach to Equation of State in Lattice QCD
A new approach to study the equation of state in finite-temperature QCD is
proposed on the lattice. Unlike the conventional method in which the temporal
lattice size is fixed, the temperature is varied by changing at
fixed lattice scale. The pressure of the hot QCD plasma is calculated by the
integration of the trace anomaly with respect to at fixed lattice scale.
This "-integral method" is tested in quenched QCD on isotropic and
anisotropic lattices and is shown to give reliable results especially at
intermediate and low temperatures.Comment: 5 pages, ReVTeX, 4 figures, version to appear in PR
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